Differential isotropic model of ferromagnetic hysteresis

This paper presents an alternative isotropic model of magnetization curves in ferromagnetic materials. It is based on the well-known Jiles-Atherton model, but significantly modifies its assumptions to be consistent with fundamental physical principles. As a result, the number of model parameters has been reduced to four. The differential model couples the volume energy density of the sample with the external magnetic field and includes the process of rigid and flexible overcoming of the pinning sites in the law of energy density conservation. The magnetic moment magnitude is connected with coherent regions called magnetic clusters, which are smaller than magnetic domains. The commonly used concept of anhysteretic magnetization, based on the Langevin function, is modified by a parameter $\ensuremath{\beta}$, which represents the average mutual interaction among magnetic clusters. The model was successfully tested on two isotropic materials: amorphous ${\mathrm{Fe}}_{77.5}{\mathrm{Si}}_{7.5}{\mathrm{B}}_{15}$ alloy and powdered magnetite. The main advantages compared with previous models are the simpler model equation and a much more convenient numerical and fitting procedure.